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1 results

  • The asymptotic behavior of a divergent linear birth and death process

  • Martha J. Siegel
  • Journal:
    Advances in Applied Probability / Volume 8 / Issue 2 / June 1976
    Published online by Cambridge University Press:
    01 July 2016, pp. 315-338
    Print publication:
    June 1976

  • We consider a birth and death process with Q-matrix of rates qm,m + 1 = mβ, qm,m − 1 = mδ, qm,m = – m(β + δ) and qm,n = 0 otherwise. We assume that 0 < δ < β and β – δ = 1. The asymptotic behavior of first-arrival time at state n given that the process is at state m at time zero is expressed in terms of polynomials and it is shown that if m < n and m is large that the first-arrival time is close to log n/m with high probability.